2 Answers
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There are many different ways to make a spindle in plants: "Mitotic spindles may be organized at centriolar centrosomes (only in final divisions of spermatogenesis), polar organizers (POs), plastid MTOCs, or nuclear envelope MTOCs (NE-MTOCs)." Of these, only the latter has been observed in angiosperms (flowering plants). For more info (and the source of the quote), see Brown & Lemmon, "The Pleiomorphic Plant MTOC: An Evolutionary Perspective"

Plant cells without centrioles build special vesicles from their Golgi apparatus which are important for cell division.

This website has a nice comparison of different modes of cell division. Look for "Cytokinesis by Phragmoplasts" to get to the relevant part. Phragmoplasts are not exactly a replacement for centrioles, but the whole process is a little different.